Regulators of electric machines, such as voltage regulator of a DC generator of a motor vehicle, are generally mounted in the vicinity of the electric machine; thus, they have to be cooled in order to avoid damage to heat-sensitive electronic components of the regulator resulting from the heat generated during the operation of the electric machine. For this reason, voltage regulators of motor vehicles mounted on the generator are provided with a cooling body made of a good heat conductive material on their side facing away from the generator, which, during the operation of the generator, has applied to it a cooling air stream from a cooling air fan driven by the generator. In order to improve the cooling performance, the cooling body has a plurality of smooth cooling ribs aligned generally in parallel to one another on its upper side, whose surfaces form a heat exchange surface, together with the surfaces in the interstices between the cooling ribs. This heat exchange surface is aligned, with respect to the cooling air stream, in such a way that the cooling air is conducted all the way through the interstices between the cooling ribs, generally parallel to the upper side of the cooling body, past the heat exchange surface. However, boundary layers form at the heat exchange surface which impair convective heat transmission, and thus the cooling effect.